There. See ? Confirms that H1B(*) has rocked AND toppled the standard of living of American EE's, driving their standup personalities and high salaries out into the lower class.
Replaced by obedient-less qualified(resumes inflated by greedy US colleges+greedy UNpatriotic US corporations+greedy US lawmakers+'tiger' pack study groups sharing howework loads, or faked back in India or China). Do NOT let yur children be duped US colleges promising great EE careers to your kieds. US colleges are part of the H1B scam-going on 30 years. I recall in my 1st job, a grey haired Phd H1B, trying to take over my small project, claiming he was 27yrs old-my American manager loved these H1B's, though. just loved them back n 1987 !! No wonder ...

The hiring process is broken. The old saying goes "Once you have a job everyone is willing to offer you a job." The hard part is getting past HR and meeting with the people behind the doors who need help. If you don't have a job don't apply here. Great. My youngest has a B.S. in Chemistry ... no jobs for anyone 'right out of college'. Sound familiar? Entry level jobs specify 3-5 years experience. Great. If there is a shortage it is because of 'diversity'. I've witnessed over the decades that if you don't have the right 'plumbing' or 'paint job' you are not considered in the (rare) new hires process.

I recently retired from a large aerospace company, and have a couple of comments regarding the "engineer shortage". First, over the last few years of my career, my employer outsourced the recruiting function. The company chosen was not technically savvy (related to me by friends who I suggested apply for open engineering positions). As has been related in other responses, such recruiters (maybe company HR personnel as well) abdicate the filtering task to a software "key word matching" program. Thus, only applicants who have mastered the art of buzz word resume construction make it through the filter.
Secondly, over the last few years, my employer off-shored as many engineering design jobs as possible, and did as much as possible to force the remaining engineers (especially senior staff) to leave. Any high school student bright enough to survive an engineering curriculum is also bright enough to see the limited employment future with large US companies. My employer is not unique in this regard, many of the largest employers of engineers are following the same practice.
I'm glad I've retired, and my career was good to me; financially in that I could retire, intellectually because keeping up with the ever changing technology provided mental challenges and growth, and I got to create some really cool products and work with some really neat technologies. Not sure similar opportunities exist today.

There is much truth to the HR "cookie cutter" filter folks; applicant "A" doesn't fully meet the stated qualifications for the req so reject him.
But Let applicant "A" actually talk with the engineers and technical management who opened the req in the first place and you'll experience totally different hiring outcomes.
Companies don't want to spend the money to do on the job training despite the fact that nearly every employee needs some time/training to become proficient in a particular company's processes and procedures;
proficiency in the latest EDA design flows is necessary but not sufficient to ensure the recent hire will be productive.
After all, bright, talented people can master any tool but mastery of a tool doesn't imply brightness, talent or ability to make a contribution.

Starting a company is no longer an option. I know many people that have tried that strategy, and the minute your product hits the marketplace, unless it is patented, cheap clones will put you out of business. And even patent protection is not foolproof. It's easy for big corporations to do a workaround.
The solution is an import duty on products from foreign companies that do not play by the rules. How can you compete with foreign companies that have masses of workers in dormitories ready to work 14-16 hour days at a moments notice?
If the playing field is level, we can compete. But it's not.

This same debate happens every few years when there are big layoffs in the industry. This time is different. The jobs are not coming back...
What's the point of a STEM education if there are no jobs or stable career prospects. Better to go to a trade school and learn to be an electrician or a plumber. At least you can support a family.
This is the sad state of affairs due to free market nuts who dismissed engineers being required to have licenses years ago when we had a chance to prevent this disaster. Now, companies are free to layoff good local engineers and hire cheaper offshore ones. They can do this as long as technology remains stagnant -- which is guaranteed with less funding for basic research under Republican administrations. Technology stagnation gives offshore engineers time to come up to speed on current practices.
This should be seen as a national security issue. Fewer trained engineers means we will loose our technology edge in defense and open ourselves up to cyber attacks by allowing foreign equipment to be installed in our telecom networks.
I urge anyone who is out of work and and looking for a job to start a company in your garage/basement. Don't just sit there waiting for some politician to solve your problems. Things will get a lot worse before they get better.

Nice recap of what was said in the many posts.
Just one point, though. I'm not so sure that the majority non-technically-inclined teachers is such a big obstacle. I, for one, never expected my teachers, certainly not through grade school, to be interested in what I enthused over. But kids who care about anything have a way of pursuing these things on their own. No matter what subject matter.
It does matter more in high school, because you need the basics down cold to make it to college STEM majors.
As to what other kids think is cool? Egad. Anyone who gets dissuaded by that wouldn't have the stamina to stick it out anyway.